ELLIPTIC EQUATIONS IN DIVERGENCE FORM WITH DISCONTINUOUS COEFFICIENTS IN DOMAINS WITH CORNERS*

doi:10.1007/s10473-024-0515-2

数学物理学报(英文版) ›› 2024, Vol. 44 ›› Issue (5): 1903-1915.doi: 10.1007/s10473-024-0515-2

ELLIPTIC EQUATIONS IN DIVERGENCE FORM WITH DISCONTINUOUS COEFFICIENTS IN DOMAINS WITH CORNERS^*

Jun Chen, Xuemei Deng^†

Three Gorges Mathematical Research Center, China Three Gorges University, Yichang 443002, China

收稿日期:2022-11-20 修回日期:2024-06-05 出版日期:2024-10-25 发布日期:2024-10-22
通讯作者: †Xuemei Deng, E-mail,: dxuemei@ctgu.edu.cn
作者简介:Jun Chen, E-mail,: chenjun4@ctgu.edu.cn
基金资助:
Chen's research was supported by National Natural Science Foundation of China (12061080, 12161087 and 12261093) and the Science and Technology Project of the Education Department of Jiangxi Province (GJJ211601). Deng's research was supported by National Natural Science Foundation of China (11871305).

ELLIPTIC EQUATIONS IN DIVERGENCE FORM WITH DISCONTINUOUS COEFFICIENTS IN DOMAINS WITH CORNERS^*

Jun Chen, Xuemei Deng^†

Three Gorges Mathematical Research Center, China Three Gorges University, Yichang 443002, China

Received:2022-11-20 Revised:2024-06-05 Online:2024-10-25 Published:2024-10-22
Contact: †Xuemei Deng, E-mail,: dxuemei@ctgu.edu.cn
About author:Jun Chen, E-mail,: chenjun4@ctgu.edu.cn
Supported by:
Chen's research was supported by National Natural Science Foundation of China (12061080, 12161087 and 12261093) and the Science and Technology Project of the Education Department of Jiangxi Province (GJJ211601). Deng's research was supported by National Natural Science Foundation of China (11871305).

摘要/Abstract

摘要： We study equations in divergence form with piecewise $C^{\alpha }$ coefficients. The domains contain corners and the discontinuity surfaces are attached to the edges of the corners. We obtain piecewise $C^{1,\alpha }$ estimates across the discontinuity surfaces and provide an example to illustrate the issue regarding the regularity at the corners.

关键词: elliptic equations, divergence form, discontinuous coefficients, corner regularity

Abstract: We study equations in divergence form with piecewise $C^{\alpha }$ coefficients. The domains contain corners and the discontinuity surfaces are attached to the edges of the corners. We obtain piecewise $C^{1,\alpha }$ estimates across the discontinuity surfaces and provide an example to illustrate the issue regarding the regularity at the corners.

Key words: elliptic equations, divergence form, discontinuous coefficients, corner regularity

中图分类号:

35J15

Jun Chen, Xuemei Deng. ELLIPTIC EQUATIONS IN DIVERGENCE FORM WITH DISCONTINUOUS COEFFICIENTS IN DOMAINS WITH CORNERS^*[J]. 数学物理学报(英文版), 2024, 44(5): 1903-1915.

Jun Chen, Xuemei Deng. ELLIPTIC EQUATIONS IN DIVERGENCE FORM WITH DISCONTINUOUS COEFFICIENTS IN DOMAINS WITH CORNERS^*[J]. Acta mathematica scientia,Series B, 2024, 44(5): 1903-1915.

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ELLIPTIC EQUATIONS IN DIVERGENCE FORM WITH DISCONTINUOUS COEFFICIENTS IN DOMAINS WITH CORNERS^*

ELLIPTIC EQUATIONS IN DIVERGENCE FORM WITH DISCONTINUOUS COEFFICIENTS IN DOMAINS WITH CORNERS^*

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